CheckViz: Sanity Check and Topological Clues for Linear and Non-Linear Mappings

Multidimensional scaling is a must-have tool for visual data miners, projecting multidimensional data onto a two-dimensional plane. However, what we see is not necessarily what we think about. In many cases, end-users do not take care of scaling the projection space with respect to the multidimensional space. Anyway, when using nonlinear mappings, scaling is not even possible. Yet, without scaling geometrical structures which might appear do not make more sense than considering a random map. Without scaling, we shall not make inference from the display back to the multidimensional space. No clusters, no trends, no outliers, there is nothing to infer without first quantifying the mapping quality. Several methods to qualify mappings have been devised. Here, we propose CheckViz, a new method belonging to the framework of Verity Visualization [WPL95]. We define a twodimensional perceptually uniform colour coding which allows visualising tears and false neighbourhoods, the two elementary and complementary types of geometrical mapping distortions, straight onto the map at the location where they occur. As examples shall demonstrate, this visualisation method is essential to help users make sense out of the mappings and to prevent them from over interpretations. It could be applied to check other mappings as well. Categories and subject descriptors: multidimensional data; nonlinear mapping; multidimensional scaling; evaluation; quality visualisation